In order to eliminate or at least reduce intersymbol interference in ditigal modems, it is necessary, in accordance with normal design techniques, to filter the signal through a low-pass filter system with a raised-cosine (RC) characteristic having a cut-off frequency equal to one-half the baud rate. This filtering ideally causes all sample impulses other than that of the current sample to have a null at the sample time, thus leaving a clean, unambiguous current sample.
Normally, this RC filtering is implemented by using a .sqroot.RC filter (i.e. a filter with a characteristic which is the square root of a raised cosine) in the transmitter and a .sqroot.RC filter in the receiver. Inasmuch as the overall filter characteristic is the product of the two, RC filtering results.
For acceptable levels of filtering, (i.e. out-of-band energy suppression), a relatively large number of filter taps are sometimes required. Inasmuch as each tap requires a multiplying operation, considerable computing power is required in a high-quality conventional FIR filter. Even with an increasing trend towards the requirement of more stringent filtering, this can become a problem. Consequently, there is a need for a filtering scheme which reduces the number of taps needed for a given filtering quality level.